A rod of length 80 cm rotates about its mid point with a frequency of 10 rev/s. The potential difference in volts) between two ends of the rod due to a magnetic field, B=0.5 T directed perpendicular to the rod is

Options

A. `pi`
B. `1.6 pi`
C. `2 pi`
D. `0.8 pi`

Answer

B

Explanation

Given,
Length of rod, `L = 80 cm =0.8 m`
Rrequency of rod, f = 10 rev/s
Magnetic field, `B == 0.5 T`
Potential difference between two ends of the rod due to magnetic fields is given by,
`V = 2xx` potential difference between centre of rod and one end of rod
` =2 xx ("Change in flux")/("time")`
`= 2 xx ( B pi r ^(2))/(T)`
` = 2xx B pi rau^(2) f`
`= 2 xx 0.5 xx pi xx ((L )/(2)) ^(2) xx 10 (because r = (L)/(2))`
`= 10 pi ((0.8)/(2)) ^(2) `
` = 10 pi xx 0.16`
`therefore B = 1.6 pi`